Ruben wants to plant a rectangular vegetable garden. He will use a patch of land that is 3 times as long as it is wide. Ruben also decides to leave a 3-inch border along the perimeter of the garden, where nothing will be planted. This leaves Ruben with a total planting area of 180 square inches.

Which equation correctly describes the available planting area for the vegetable garden?






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1 Answer

The total garden including the border has dimension 3x by x where x is the width in inches.

The dimensions of the growing area are reduced by 6 inches (3 inches on each side) so its dimensions are 3x-6 by x-6 and the equation for the area is 180=(3x-6)(x-6)=3x²-24x+36, answer option 2.

(Although the question doesn’t ask for it we get the equation 3x²-24x-144=0, which reduces to x²-8x-48=0=(x-12)(x+4), so x=12 inches and the dimensions are 12 by 36 inches, with the growing area 6 by 30 inches.)

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